arXiv subjects

Sylvain Barbot

Publications and source records attributed to Sylvain Barbot.

4 recordsLinked to original sources

arXiv2018

Deformation of a Half-Space from Anelastic Strain Confined in a Tetrahedral Volume

Deformation in the lithosphere-asthenosphere system can be accommodated by faulting and plastic flow. However, incorporating structural data in models of distributed deformation still represents a challenge. Here, I present solutions for the displacements and stress in a half-space caused by distributed anelastic strain confined in a tetrahedral volume. These solutions form the basis of curvilinear meshes that can adapt to realistic structural settings, such as a mantle wedge corner, a spherical shell around a magma chamber, or an aquifer. I provide computer programs to evaluate them in the cases of anti-plane strain, in-plane strain, and three-dimensional deformation. These tools may prove useful in the modeling of deformation data in tectonics, volcanology, and hydrology.

physics.geo-ph↗

arXiv2018

Fast, accurate solutions for curvilinear earthquake faults and anelastic strain

Imaging the anelastic deformation within the crust and lithosphere using surface geophysical data remains a significant challenge in part due to the wide range of physical processes operating at different depths and to various levels of localization that they embody. Models of Earth's elastic properties from seismological imaging combined with geodetic modeling may form the basis of comprehensive rheological models of Earth's interior. However, representing the structural complexity of faults and shear zones in numerical models of deformation still constitutes a major difficulty. Here, we present numerical techniques for high-precision models of deformation and stress around both curvilinear faults and volumes undergoing anelastic (irreversible) strain in a heterogenous elastic half-space. To that end, we enhance the software Gamra to model triangular and rectangular fault patches and tetrahedral and cuboidal strain volumes. This affords a means of rapid and accurate calculations of elasto-static Green's functions for localized (e.g., faulting) and distributed (e.g., viscoelastic) deformation in Earth's crust and lithosphere. We demonstrate the correctness of the method with analytic tests, and we illustrate its practical performance by solving for coseismic and postseismic deformation following the 2015 Mw 7.8 Gorkha, Nepal earthquake to extremely high precision.

physics.geo-ph↗

arXiv2018

Gamra: Simple Meshes for Complex Earthquakes

The static offsets caused by earthquakes are well described by elastostatic models with a discontinuity in the displacement along the fault. A traditional approach to model this discontinuity is to align the numerical mesh with the fault and solve the equations using finite elements. However, this distorted mesh can be difficult to generate and update. We present a new numerical method, inspired by the Immersed Interface Method, for solving the elastostatic equations with embedded discontinuities. This method has been carefully designed so that it can be used on parallel machines on an adapted finite difference grid. We have implemented this method in Gamra, a new code for earth modelling. We demonstrate the correctness of the method with analytic tests, and we demonstrate its practical performance by solving a realistic earthquake model to extremely high precision.

physics.geo-ph↗

arXiv2018

On the relation between plasticity, friction, and geometry

Plasticity refers to thermodynamically irreversible deformation associated with a change of configuration of materials. Friction is a phenomenological law that describes the forces resisting sliding between two solids or across an embedded dislocation. These two types of constitutive behaviors explain the deformation of a wide range of engineered and natural materials. Yet, they are typically described with distinct physical laws that cloud their inherent connexion. Here, I introduce a multiplicative form of kinematic friction that closely resembles the power-law flow of viscoplastic materials and that regularizes the constitutive behavior at vanishing velocity, with important implications for rupture dynamics. Using a tensor-valued state variable that describes the degree of localization, I describe a constitutive framework compatible with viscoplastic theories that captures the continuum between distributed and localized deformation and for which the frictional response emerges when the deformed region collapses from three to two dimensions.

physics.geo-ph↗